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bssn_rhs(fortran): migrate C kernel loop-fusion optimizations

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CGH0S7
2026-03-03 15:41:26 +08:00
parent b35e1b289f
commit d310ef918b
1 changed files with 268 additions and 216 deletions
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AMSS_NCKU_source/bssn_rhs.f90
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@@ -62,6 +62,7 @@
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
! gont = 0: success; gont = 1: something wrong
integer::gont
integer :: i,j,k
!~~~~~~> Other variables:
@@ -85,6 +86,11 @@
real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
real*8 :: dX, dY, dZ, PI
real*8 :: divb_loc,det_loc
real*8 :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
real*8 :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
real*8 :: fxx_loc,fxy_loc,fxz_loc
real*8 :: Gamxa_loc,Gamya_loc,Gamza_loc
real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
@@ -97,7 +103,7 @@
#endif
#if (GAUGE == 6 || GAUGE == 7)
integer :: BHN,i,j,k
integer :: BHN
real*8, dimension(9) :: Porg
real*8, dimension(3) :: Mass
real*8 :: r1,r2,M,A,w1,w2,C1,C2
@@ -145,22 +151,24 @@
dY = Y(2) - Y(1)
dZ = Z(2) - Z(1)
alpn1 = Lap + ONE
chin1 = chi + ONE
gxx = dxx + ONE
gyy = dyy + ONE
gzz = dzz + ONE
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
alpn1(i,j,k) = Lap(i,j,k) + ONE
chin1(i,j,k) = chi(i,j,k) + ONE
gxx(i,j,k) = dxx(i,j,k) + ONE
gyy(i,j,k) = dyy(i,j,k) + ONE
gzz(i,j,k) = dzz(i,j,k) + ONE
enddo
enddo
enddo
call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
div_beta = betaxx + betayy + betazz
call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
@@ -168,151 +176,179 @@
call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
gxx_rhs = - TWO * alpn1 * Axx - F2o3 * gxx * div_beta + &
TWO *( gxx * betaxx + gxy * betayx + gxz * betazx)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
div_beta(i,j,k) = divb_loc
gyy_rhs = - TWO * alpn1 * Ayy - F2o3 * gyy * div_beta + &
TWO *( gxy * betaxy + gyy * betayy + gyz * betazy)
chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
gzz_rhs = - TWO * alpn1 * Azz - F2o3 * gzz * div_beta + &
TWO *( gxz * betaxz + gyz * betayz + gzz * betazz)
gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
TWO * ( gxx(i,j,k) * betaxx(i,j,k) + gxy(i,j,k) * betayx(i,j,k) + gxz(i,j,k) * betazx(i,j,k) )
gxy_rhs = - TWO * alpn1 * Axy + F1o3 * gxy * div_beta + &
gxx * betaxy + gxz * betazy + &
gyy * betayx + gyz * betazx &
- gxy * betazz
gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
TWO * ( gxy(i,j,k) * betaxy(i,j,k) + gyy(i,j,k) * betayy(i,j,k) + gyz(i,j,k) * betazy(i,j,k) )
gyz_rhs = - TWO * alpn1 * Ayz + F1o3 * gyz * div_beta + &
gxy * betaxz + gyy * betayz + &
gxz * betaxy + gzz * betazy &
- gyz * betaxx
gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
TWO * ( gxz(i,j,k) * betaxz(i,j,k) + gyz(i,j,k) * betayz(i,j,k) + gzz(i,j,k) * betazz(i,j,k) )
gxz_rhs = - TWO * alpn1 * Axz + F1o3 * gxz * div_beta + &
gxx * betaxz + gxy * betayz + &
gyz * betayx + gzz * betazx &
- gxz * betayy !rhs for gij
gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
! invert tilted metric
gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
gxz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axz(i,j,k) + F1o3 * gxz(i,j,k) * divb_loc + &
gxx(i,j,k) * betaxz(i,j,k) + gxy(i,j,k) * betayz(i,j,k) + gyz(i,j,k) * betayx(i,j,k) + &
gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
det_loc = gxx(i,j,k) * gyy(i,j,k) * gzz(i,j,k) + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) + &
gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
gupyy_loc = ( gxx(i,j,k) * gzz(i,j,k) - gxz(i,j,k) * gxz(i,j,k) ) / det_loc
gupyz_loc = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / det_loc
gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
gupxx(i,j,k) = gupxx_loc
gupxy(i,j,k) = gupxy_loc
gupxz(i,j,k) = gupxz_loc
gupyy(i,j,k) = gupyy_loc
gupyz(i,j,k) = gupyz_loc
gupzz(i,j,k) = gupzz_loc
if(co == 0)then
! Gam^i_Res = Gam^i + gup^ij_,j
Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
+gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
+gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
+gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
+gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
+gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
+gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
+gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
+gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
+gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
+gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
+gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
+gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
Gmz_Res(i,j,k) = Gamz(i,j,k) - ( &
gupxx_loc*(gupxz_loc*gxxx(i,j,k)+gupyz_loc*gxyx(i,j,k)+gupzz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
gupyy_loc*(gupxz_loc*gxyy(i,j,k)+gupyz_loc*gyyy(i,j,k)+gupzz_loc*gyzy(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxzy(i,j,k)+gupyz_loc*gyzy(i,j,k)+gupzz_loc*gzzy(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
endif
! second kind of connection
Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
Gamxxx(i,j,k)=HALF*( gupxx_loc*gxxx(i,j,k) + gupxy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupxz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamyxx(i,j,k)=HALF*( gupxy_loc*gxxx(i,j,k) + gupyy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupyz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamzxx(i,j,k)=HALF*( gupxz_loc*gxxx(i,j,k) + gupyz_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupzz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
Gamxyy(i,j,k)=HALF*( gupxx_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupxy_loc*gyyy(i,j,k) + gupxz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamyyy(i,j,k)=HALF*( gupxy_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyy_loc*gyyy(i,j,k) + gupyz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamzyy(i,j,k)=HALF*( gupxz_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyz_loc*gyyy(i,j,k) + gupzz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
Gamxzz(i,j,k)=HALF*( gupxx_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupxy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupxz_loc*gzzz(i,j,k))
Gamyzz(i,j,k)=HALF*( gupxy_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupyz_loc*gzzz(i,j,k))
Gamzzz(i,j,k)=HALF*( gupxz_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyz_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupzz_loc*gzzz(i,j,k))
Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
Gamxxy(i,j,k)=HALF*( gupxx_loc*gxxy(i,j,k) + gupxy_loc*gyyx(i,j,k) + gupxz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamyxy(i,j,k)=HALF*( gupxy_loc*gxxy(i,j,k) + gupyy_loc*gyyx(i,j,k) + gupyz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamzxy(i,j,k)=HALF*( gupxz_loc*gxxy(i,j,k) + gupyz_loc*gyyx(i,j,k) + gupzz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
Gamxxz(i,j,k)=HALF*( gupxx_loc*gxxz(i,j,k) + gupxy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupxz_loc*gzzx(i,j,k) )
Gamyxz(i,j,k)=HALF*( gupxy_loc*gxxz(i,j,k) + gupyy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupyz_loc*gzzx(i,j,k) )
Gamzxz(i,j,k)=HALF*( gupxz_loc*gxxz(i,j,k) + gupyz_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupzz_loc*gzzx(i,j,k) )
Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
Gamxyz(i,j,k)=HALF*( gupxx_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupxy_loc*gyyz(i,j,k) + gupxz_loc*gzzy(i,j,k) )
Gamyyz(i,j,k)=HALF*( gupxy_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyy_loc*gyyz(i,j,k) + gupyz_loc*gzzy(i,j,k) )
Gamzyz(i,j,k)=HALF*( gupxz_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyz_loc*gyyz(i,j,k) + gupzz_loc*gzzy(i,j,k) )
enddo
enddo
enddo
! Raise indices of \tilde A_{ij} and store in R_ij
Rxx = gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
Ryy = gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
Rzz = gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
Rxy = gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
(gupxx * gupyy + gupxy * gupxy)* Axy + &
(gupxx * gupyz + gupxz * gupxy)* Axz + &
(gupxy * gupyz + gupxz * gupyy)* Ayz
Rxz = gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
(gupxx * gupyz + gupxy * gupxz)* Axy + &
(gupxx * gupzz + gupxz * gupxz)* Axz + &
(gupxy * gupzz + gupxz * gupyz)* Ayz
Ryz = gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
(gupxy * gupyz + gupyy * gupxz)* Axy + &
(gupxy * gupzz + gupyz * gupxz)* Axz + &
(gupyy * gupzz + gupyz * gupyz)* Ayz
! Right hand side for Gam^i without shift terms...
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
gupxx_loc = gupxx(i,j,k)
gupxy_loc = gupxy(i,j,k)
gupxz_loc = gupxz(i,j,k)
gupyy_loc = gupyy(i,j,k)
gupyz_loc = gupyz(i,j,k)
gupzz_loc = gupzz(i,j,k)
Gamx_rhs = - TWO * ( Lapx * Rxx + Lapy * Rxy + Lapz * Rxz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxx + chiy * Rxy + chiz * Rxz ) - &
gupxx * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupxy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupxz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz + &
TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
Rxx_loc = gupxx_loc * gupxx_loc * Axx(i,j,k) + gupxy_loc * gupxy_loc * Ayy(i,j,k) + gupxz_loc * gupxz_loc * Azz(i,j,k) + &
TWO * (gupxx_loc * gupxy_loc * Axy(i,j,k) + gupxx_loc * gupxz_loc * Axz(i,j,k) + gupxy_loc * gupxz_loc * Ayz(i,j,k))
Ryy_loc = gupxy_loc * gupxy_loc * Axx(i,j,k) + gupyy_loc * gupyy_loc * Ayy(i,j,k) + gupyz_loc * gupyz_loc * Azz(i,j,k) + &
TWO * (gupxy_loc * gupyy_loc * Axy(i,j,k) + gupxy_loc * gupyz_loc * Axz(i,j,k) + gupyy_loc * gupyz_loc * Ayz(i,j,k))
Rzz_loc = gupxz_loc * gupxz_loc * Axx(i,j,k) + gupyz_loc * gupyz_loc * Ayy(i,j,k) + gupzz_loc * gupzz_loc * Azz(i,j,k) + &
TWO * (gupxz_loc * gupyz_loc * Axy(i,j,k) + gupxz_loc * gupzz_loc * Axz(i,j,k) + gupyz_loc * gupzz_loc * Ayz(i,j,k))
Rxy_loc = gupxx_loc * gupxy_loc * Axx(i,j,k) + gupxy_loc * gupyy_loc * Ayy(i,j,k) + gupxz_loc * gupyz_loc * Azz(i,j,k) + &
(gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
(gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
(gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
Rxz_loc = gupxx_loc * gupxz_loc * Axx(i,j,k) + gupxy_loc * gupyz_loc * Ayy(i,j,k) + gupxz_loc * gupzz_loc * Azz(i,j,k) + &
(gupxx_loc * gupyz_loc + gupxy_loc * gupxz_loc) * Axy(i,j,k) + &
(gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
(gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
Ryz_loc = gupxy_loc * gupxz_loc * Axx(i,j,k) + gupyy_loc * gupyz_loc * Ayy(i,j,k) + gupyz_loc * gupzz_loc * Azz(i,j,k) + &
(gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
(gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
(gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
Rxx(i,j,k) = Rxx_loc
Ryy(i,j,k) = Ryy_loc
Rzz(i,j,k) = Rzz_loc
Rxy(i,j,k) = Rxy_loc
Rxz(i,j,k) = Rxz_loc
Ryz(i,j,k) = Ryz_loc
Gamy_rhs = - TWO * ( Lapx * Rxy + Lapy * Ryy + Lapz * Ryz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxy + chiy * Ryy + chiz * Ryz ) - &
gupxy * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupyz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz + &
TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
gupxx_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupxy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupxz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamxxx(i,j,k) * Rxx_loc + Gamxyy(i,j,k) * Ryy_loc + Gamxzz(i,j,k) * Rzz_loc + &
TWO * (Gamxxy(i,j,k) * Rxy_loc + Gamxxz(i,j,k) * Rxz_loc + Gamxyz(i,j,k) * Ryz_loc))
Gamz_rhs = - TWO * ( Lapx * Rxz + Lapy * Ryz + Lapz * Rzz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxz + chiy * Ryz + chiz * Rzz ) - &
gupxz * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyz * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupzz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz + &
TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
Gamy_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxy_loc + Lapy(i,j,k) * Ryy_loc + Lapz(i,j,k) * Ryz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxy_loc + chiy(i,j,k) * Ryy_loc + chiz(i,j,k) * Ryz_loc) - &
gupxy_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupyy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupyz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamyxx(i,j,k) * Rxx_loc + Gamyyy(i,j,k) * Ryy_loc + Gamyzz(i,j,k) * Rzz_loc + &
TWO * (Gamyxy(i,j,k) * Rxy_loc + Gamyxz(i,j,k) * Rxz_loc + Gamyyz(i,j,k) * Ryz_loc))
Gamz_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxz_loc + Lapy(i,j,k) * Ryz_loc + Lapz(i,j,k) * Rzz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxz_loc + chiy(i,j,k) * Ryz_loc + chiz(i,j,k) * Rzz_loc) - &
gupxz_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupyz_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupzz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamzxx(i,j,k) * Rxx_loc + Gamzyy(i,j,k) * Ryy_loc + Gamzzz(i,j,k) * Rzz_loc + &
TWO * (Gamzxy(i,j,k) * Rxy_loc + Gamzxz(i,j,k) * Rxz_loc + Gamzyz(i,j,k) * Ryz_loc))
enddo
enddo
enddo
call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
@@ -321,38 +357,54 @@
call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
fxx = gxxx + gxyy + gxzz
fxy = gxyx + gyyy + gyzz
fxz = gxzx + gyzy + gzzz
Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
divb_loc = div_beta(i,j,k)
fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
Gamx_rhs = Gamx_rhs + F2o3 * Gamxa * div_beta - &
Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz + &
F1o3 * (gupxx * fxx + gupxy * fxy + gupxz * fxz ) + &
gupxx * gxxx + gupyy * gyyx + gupzz * gzzx + &
TWO * (gupxy * gxyx + gupxz * gxzx + gupyz * gyzx )
gupxx_loc = gupxx(i,j,k)
gupxy_loc = gupxy(i,j,k)
gupxz_loc = gupxz(i,j,k)
gupyy_loc = gupyy(i,j,k)
gupyz_loc = gupyz(i,j,k)
gupzz_loc = gupzz(i,j,k)
Gamy_rhs = Gamy_rhs + F2o3 * Gamya * div_beta - &
Gamxa * betayx - Gamya * betayy - Gamza * betayz + &
F1o3 * (gupxy * fxx + gupyy * fxy + gupyz * fxz ) + &
gupxx * gxxy + gupyy * gyyy + gupzz * gzzy + &
TWO * (gupxy * gxyy + gupxz * gxzy + gupyz * gyzy )
Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
Gamya_loc = gupxx_loc * Gamyxx(i,j,k) + gupyy_loc * Gamyyy(i,j,k) + gupzz_loc * Gamyzz(i,j,k) + &
TWO * (gupxy_loc * Gamyxy(i,j,k) + gupxz_loc * Gamyxz(i,j,k) + gupyz_loc * Gamyyz(i,j,k))
Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
Gamxa(i,j,k) = Gamxa_loc
Gamya(i,j,k) = Gamya_loc
Gamza(i,j,k) = Gamza_loc
Gamz_rhs = Gamz_rhs + F2o3 * Gamza * div_beta - &
Gamxa * betazx - Gamya * betazy - Gamza * betazz + &
F1o3 * (gupxz * fxx + gupyz * fxy + gupzz * fxz ) + &
gupxx * gxxz + gupyy * gyyz + gupzz * gzzz + &
TWO * (gupxy * gxyz + gupxz * gxzz + gupyz * gyzz ) !rhs for Gam^i
Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
TWO * (gupxy_loc * gxyx(i,j,k) + gupxz_loc * gxzx(i,j,k) + gupyz_loc * gyzx(i,j,k))
Gamy_rhs(i,j,k) = Gamy_rhs(i,j,k) + F2o3 * Gamya_loc * divb_loc - &
Gamxa_loc * betayx(i,j,k) - Gamya_loc * betayy(i,j,k) - Gamza_loc * betayz(i,j,k) + &
F1o3 * (gupxy_loc * fxx_loc + gupyy_loc * fxy_loc + gupyz_loc * fxz_loc) + &
gupxx_loc * gxxy(i,j,k) + gupyy_loc * gyyy(i,j,k) + gupzz_loc * gzzy(i,j,k) + &
TWO * (gupxy_loc * gxyy(i,j,k) + gupxz_loc * gxzy(i,j,k) + gupyz_loc * gyzy(i,j,k))
Gamz_rhs(i,j,k) = Gamz_rhs(i,j,k) + F2o3 * Gamza_loc * divb_loc - &
Gamxa_loc * betazx(i,j,k) - Gamya_loc * betazy(i,j,k) - Gamza_loc * betazz(i,j,k) + &
F1o3 * (gupxz_loc * fxx_loc + gupyz_loc * fxy_loc + gupzz_loc * fxz_loc) + &
gupxx_loc * gxxz(i,j,k) + gupyy_loc * gyyz(i,j,k) + gupzz_loc * gzzz(i,j,k) + &
TWO * (gupxy_loc * gxyz(i,j,k) + gupxz_loc * gxzz(i,j,k) + gupyz_loc * gyzz(i,j,k))
enddo
enddo
enddo
!first kind of connection stored in gij,k
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
@@ -948,15 +1000,15 @@
!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
! lopsided_kodis shares the symmetry_bd buffer between advection and
! dissipation, eliminating redundant full-grid copies. For metric variables
! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
! gxx/gyy/gzz (=dxx/dyy/dzz+1): stencil coefficients sum to zero,
! so the constant offset has no effect on dissipation.
call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)